In physics, the Cardy formula gives the entropy of a two-dimensional conformal field theory (CFT).
In recent years, this formula has been especially useful in the calculation of the entropy of BTZ black holes and in checking the AdS/CFT correspondence and the holographic principle.
The proof of the above formula relies on modular invariance of a Euclidean CFT on the torus.
To be precise, the microcanonical entropy (that is to say, the logarithm of the number of states in a shell of width
[3] The resulting Cardy–Verlinde formula was obtained by studying a radiation-dominated universe with the Friedmann–Lemaître–Robertson–Walker metric where R is the radius of a n-dimensional sphere at time t. The radiation is represented by a (n+1)-dimensional CFT.
The entropy of that CFT is then given by the formula where Ec is the Casimir effect, and E the total energy.
The Cardy–Verlinde formula was later shown by Kutasov and Larsen[4] to be invalid for weakly interacting CFTs.